LMFDB - Embedded newform 847.2.f.e.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.e.729.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.618034 - 1.90211i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.618034 - 1.90211i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} -2.00000 q^{10} -2.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-1.23607 - 3.80423i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-3.23607 + 2.35114i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-1.61803 - 1.17557i) q^{20} -2.00000 q^{21} -4.00000 q^{23} +(4.85410 + 3.52671i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(1.23607 + 3.80423i) q^{26} +(3.23607 - 2.35114i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-1.23607 + 3.80423i) q^{30} +(-8.09017 - 5.87785i) q^{31} +5.00000 q^{32} +4.00000 q^{34} +(-1.61803 - 1.17557i) q^{35} +(-0.309017 + 0.951057i) q^{36} +(-1.85410 - 5.70634i) q^{37} +(-6.47214 + 4.70228i) q^{39} +(1.85410 + 5.70634i) q^{40} +(1.23607 - 3.80423i) q^{41} +(1.61803 + 1.17557i) q^{42} +12.0000 q^{43} -2.00000 q^{45} +(3.23607 + 2.35114i) q^{46} +(-3.09017 + 9.51057i) q^{47} +(-0.618034 - 1.90211i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(2.47214 + 7.60845i) q^{51} +(-1.23607 + 3.80423i) q^{52} +(4.85410 + 3.52671i) q^{53} -4.00000 q^{54} +3.00000 q^{56} +(-1.85410 + 5.70634i) q^{58} +(0.618034 + 1.90211i) q^{59} +(-3.23607 + 2.35114i) q^{60} +(3.09017 + 9.51057i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-5.66312 - 4.11450i) q^{64} -8.00000 q^{65} +8.00000 q^{67} +(3.23607 + 2.35114i) q^{68} +(-2.47214 + 7.60845i) q^{69} +(0.618034 + 1.90211i) q^{70} +(9.70820 - 7.05342i) q^{71} +(2.42705 - 1.76336i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(1.61803 + 1.17557i) q^{75} +8.00000 q^{78} +(-6.47214 - 4.70228i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(-3.23607 + 2.35114i) q^{82} +(0.618034 + 1.90211i) q^{84} +(-2.47214 + 7.60845i) q^{85} +(-9.70820 - 7.05342i) q^{86} -12.0000 q^{87} -6.00000 q^{89} +(1.61803 + 1.17557i) q^{90} +(-1.23607 + 3.80423i) q^{91} +(1.23607 + 3.80423i) q^{92} +(-16.1803 + 11.7557i) q^{93} +(8.09017 - 5.87785i) q^{94} +(3.09017 - 9.51057i) q^{96} +(8.09017 + 5.87785i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + 3 q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 - 2 * q^6 + q^7 + 3 * q^8 - q^9	$ 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + 3 q^{8} - q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + q^{16} - 4 q^{17} - q^{18} - 2 q^{20} - 8 q^{21} - 16 q^{23} + 6 q^{24} + q^{25} - 4 q^{26} + 4 q^{27} - q^{28} + 6 q^{29} + 4 q^{30} - 10 q^{31} + 20 q^{32} + 16 q^{34} - 2 q^{35} + q^{36} + 6 q^{37} - 8 q^{39} - 6 q^{40} - 4 q^{41} + 2 q^{42} + 48 q^{43} - 8 q^{45} + 4 q^{46} + 10 q^{47} + 2 q^{48} - q^{49} + q^{50} - 8 q^{51} + 4 q^{52} + 6 q^{53} - 16 q^{54} + 12 q^{56} + 6 q^{58} - 2 q^{59} - 4 q^{60} - 10 q^{62} + q^{63} - 7 q^{64} - 32 q^{65} + 32 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} + 12 q^{71} + 3 q^{72} + 8 q^{73} + 6 q^{74} + 2 q^{75} + 32 q^{78} - 8 q^{79} - 2 q^{80} + 11 q^{81} - 4 q^{82} - 2 q^{84} + 8 q^{85} - 12 q^{86} - 48 q^{87} - 24 q^{89} + 2 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} + 10 q^{94} - 10 q^{96} + 10 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 - 2 * q^6 + q^7 + 3 * q^8 - q^9 - 8 * q^10 - 8 * q^12 - 4 * q^13 + q^14 + 4 * q^15 + q^16 - 4 * q^17 - q^18 - 2 * q^20 - 8 * q^21 - 16 * q^23 + 6 * q^24 + q^25 - 4 * q^26 + 4 * q^27 - q^28 + 6 * q^29 + 4 * q^30 - 10 * q^31 + 20 * q^32 + 16 * q^34 - 2 * q^35 + q^36 + 6 * q^37 - 8 * q^39 - 6 * q^40 - 4 * q^41 + 2 * q^42 + 48 * q^43 - 8 * q^45 + 4 * q^46 + 10 * q^47 + 2 * q^48 - q^49 + q^50 - 8 * q^51 + 4 * q^52 + 6 * q^53 - 16 * q^54 + 12 * q^56 + 6 * q^58 - 2 * q^59 - 4 * q^60 - 10 * q^62 + q^63 - 7 * q^64 - 32 * q^65 + 32 * q^67 + 4 * q^68 + 8 * q^69 - 2 * q^70 + 12 * q^71 + 3 * q^72 + 8 * q^73 + 6 * q^74 + 2 * q^75 + 32 * q^78 - 8 * q^79 - 2 * q^80 + 11 * q^81 - 4 * q^82 - 2 * q^84 + 8 * q^85 - 12 * q^86 - 48 * q^87 - 24 * q^89 + 2 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 + 10 * q^94 - 10 * q^96 + 10 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	0.263792	−	0.964580i	$-0.415027\pi$
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i	−0.835853	+	0.548953i	$0.815027\pi$
$3$	0.618034	−	1.90211i	0.356822	−	1.09819i	−0.598123	−	0.801404i	$-0.704087\pi$
$3$	0.618034	−	1.90211i	0.356822	−	1.09819i	0.954945	−	0.296781i	$-0.0959133\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	−0.163928	−	0.986472i	$-0.552416\pi$
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	0.887535	+	0.460741i	$0.152416\pi$
$6$	−1.61803	+	1.17557i	−0.660560	+	0.479925i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−0.927051	+	2.85317i	−0.327762	+	1.00875i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−2.00000			−0.632456
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−3.23607	−	2.35114i	−0.897524	−	0.652089i	0.0403050	−	0.999187i	$-0.487167\pi$
$13$	−3.23607	−	2.35114i	−0.897524	−	0.652089i	−0.937829	+	0.347098i	$0.887167\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	−1.23607	−	3.80423i	−0.319151	−	0.982247i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−3.23607	+	2.35114i	−0.784862	+	0.570235i	−0.906434	−	0.422347i	$-0.861206\pi$
$17$	−3.23607	+	2.35114i	−0.784862	+	0.570235i	0.121572	+	0.992583i	$0.461206\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−1.61803	−	1.17557i	−0.361803	−	0.262866i
$21$	−2.00000			−0.436436
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	4.85410	+	3.52671i	0.990839	+	0.719887i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	1.23607	+	3.80423i	0.242413	+	0.746070i
$27$	3.23607	−	2.35114i	0.622782	−	0.452477i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	−0.961958	−	0.273196i	$-0.911919\pi$
$29$	−1.85410	−	5.70634i	−0.344298	−	1.05964i	0.617660	−	0.786445i	$-0.288081\pi$
$30$	−1.23607	+	3.80423i	−0.225674	+	0.694553i
$31$	−8.09017	−	5.87785i	−1.45304	−	1.05569i	−0.985110	−	0.171927i	$-0.945001\pi$
$31$	−8.09017	−	5.87785i	−1.45304	−	1.05569i	−0.467928	−	0.883767i	$-0.654999\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	4.00000			0.685994
$35$	−1.61803	−	1.17557i	−0.273498	−	0.198708i
$36$	−0.309017	+	0.951057i	−0.0515028	+	0.158509i
$37$	−1.85410	−	5.70634i	−0.304812	−	0.938116i	−0.979747	−	0.200239i	$-0.935828\pi$
$37$	−1.85410	−	5.70634i	−0.304812	−	0.938116i	0.674935	−	0.737878i	$-0.264172\pi$
$38$		0			0
$39$	−6.47214	+	4.70228i	−1.03637	+	0.752968i
$40$	1.85410	+	5.70634i	0.293159	+	0.902251i
$41$	1.23607	−	3.80423i	0.193041	−	0.594120i	−0.806952	−	0.590616i	$-0.798885\pi$
$41$	1.23607	−	3.80423i	0.193041	−	0.594120i	0.999994	−	0.00350392i	$-0.00111533\pi$
$42$	1.61803	+	1.17557i	0.249668	+	0.181394i
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$	3.23607	+	2.35114i	0.477132	+	0.346657i
$47$	−3.09017	+	9.51057i	−0.450748	+	1.38726i	0.425308	+	0.905049i	$0.360166\pi$
$47$	−3.09017	+	9.51057i	−0.450748	+	1.38726i	−0.876056	+	0.482210i	$0.839834\pi$
$48$	−0.618034	−	1.90211i	−0.0892055	−	0.274546i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$	2.47214	+	7.60845i	0.346168	+	1.06540i
$52$	−1.23607	+	3.80423i	−0.171412	+	0.527551i
$53$	4.85410	+	3.52671i	0.666762	+	0.484431i	0.868940	−	0.494918i	$-0.164802\pi$
$53$	4.85410	+	3.52671i	0.666762	+	0.484431i	−0.202178	+	0.979349i	$0.564802\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	3.00000			0.400892
$57$		0			0
$58$	−1.85410	+	5.70634i	−0.243456	+	0.749279i
$59$	0.618034	+	1.90211i	0.0804612	+	0.247634i	0.983193	−	0.182570i	$-0.0584416\pi$
$59$	0.618034	+	1.90211i	0.0804612	+	0.247634i	−0.902732	+	0.430204i	$0.858442\pi$
$60$	−3.23607	+	2.35114i	−0.417775	+	0.303531i
$61$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$61$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$62$	3.09017	+	9.51057i	0.392452	+	1.20784i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	−8.00000			−0.992278
$66$		0			0
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	3.23607	+	2.35114i	0.392431	+	0.285118i
$69$	−2.47214	+	7.60845i	−0.297610	+	0.915950i
$70$	0.618034	+	1.90211i	0.0738692	+	0.227346i
$71$	9.70820	−	7.05342i	1.15215	−	0.837087i	0.163386	−	0.986562i	$-0.447758\pi$
$71$	9.70820	−	7.05342i	1.15215	−	0.837087i	0.988766	+	0.149475i	$0.0477583\pi$
$72$	2.42705	−	1.76336i	0.286031	−	0.207813i
$73$	−2.47214	−	7.60845i	−0.289342	−	0.890502i	−0.985064	−	0.172191i	$-0.944915\pi$
$73$	−2.47214	−	7.60845i	−0.289342	−	0.890502i	0.695722	−	0.718311i	$-0.255085\pi$
$74$	−1.85410	+	5.70634i	−0.215535	+	0.663348i
$75$	1.61803	+	1.17557i	0.186834	+	0.135743i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−6.47214	−	4.70228i	−0.728172	−	0.529048i	0.160813	−	0.986985i	$-0.448589\pi$
$79$	−6.47214	−	4.70228i	−0.728172	−	0.529048i	−0.888985	+	0.457937i	$0.848589\pi$
$80$	0.618034	−	1.90211i	0.0690983	−	0.212663i
$81$	−3.39919	−	10.4616i	−0.377687	−	1.16240i
$82$	−3.23607	+	2.35114i	−0.357364	+	0.259640i
$83$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$83$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$84$	0.618034	+	1.90211i	0.0674330	+	0.207538i
$85$	−2.47214	+	7.60845i	−0.268141	+	0.825253i
$86$	−9.70820	−	7.05342i	−1.04686	−	0.760590i
$87$	−12.0000			−1.28654
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.61803	+	1.17557i	0.170556	+	0.123916i
$91$	−1.23607	+	3.80423i	−0.129575	+	0.398791i
$92$	1.23607	+	3.80423i	0.128869	+	0.396618i
$93$	−16.1803	+	11.7557i	−1.67782	+	1.21901i
$94$	8.09017	−	5.87785i	0.834437	−	0.606254i
$95$		0			0
$96$	3.09017	−	9.51057i	0.315389	−	0.970668i
$97$	8.09017	+	5.87785i	0.821432	+	0.596806i	0.917122	−	0.398606i	$-0.130506\pi$
$97$	8.09017	+	5.87785i	0.821432	+	0.596806i	−0.0956901	+	0.995411i	$0.530506\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	1.00000			0.100000
$101$	3.23607	+	2.35114i	0.322001	+	0.233947i	0.737029	−	0.675861i	$-0.236228\pi$
$101$	3.23607	+	2.35114i	0.322001	+	0.233947i	−0.415028	+	0.909809i	$0.636228\pi$
$102$	2.47214	−	7.60845i	0.244778	−	0.753349i
$103$	4.32624	+	13.3148i	0.426277	+	1.31195i	0.901766	+	0.432224i	$0.142271\pi$
$103$	4.32624	+	13.3148i	0.426277	+	1.31195i	−0.475489	+	0.879721i	$0.657729\pi$
$104$	9.70820	−	7.05342i	0.951968	−	0.691645i
$105$	−3.23607	+	2.35114i	−0.315808	+	0.229448i
$106$	−1.85410	−	5.70634i	−0.180086	−	0.554249i
$107$	3.70820	−	11.4127i	0.358486	−	1.10331i	−0.595475	−	0.803374i	$-0.703036\pi$
$107$	3.70820	−	11.4127i	0.358486	−	1.10331i	0.953961	−	0.299932i	$-0.0969638\pi$
$108$	−3.23607	−	2.35114i	−0.311391	−	0.226239i
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	5.56231	−	17.1190i	0.523258	−	1.61042i	−0.244478	−	0.969655i	$-0.578617\pi$
$113$	5.56231	−	17.1190i	0.523258	−	1.61042i	0.767736	−	0.640767i	$-0.221383\pi$
$114$		0			0
$115$	−6.47214	+	4.70228i	−0.603530	+	0.438490i
$116$	−4.85410	+	3.52671i	−0.450692	+	0.327447i
$117$	1.23607	+	3.80423i	0.114275	+	0.351701i
$118$	0.618034	−	1.90211i	0.0568946	−	0.175104i
$119$	3.23607	+	2.35114i	0.296650	+	0.215529i
$120$	12.0000			1.09545
$121$		0			0
$122$		0			0
$123$	−6.47214	−	4.70228i	−0.583573	−	0.423990i
$124$	−3.09017	+	9.51057i	−0.277505	+	0.854074i
$125$	3.70820	+	11.4127i	0.331672	+	1.02078i
$126$	0.809017	−	0.587785i	0.0720730	−	0.0523641i
$127$	−6.47214	+	4.70228i	−0.574309	+	0.417260i	−0.836668	−	0.547710i	$-0.815500\pi$
$127$	−6.47214	+	4.70228i	−0.574309	+	0.417260i	0.262359	+	0.964970i	$0.415500\pi$
$128$	−0.927051	−	2.85317i	−0.0819405	−	0.252187i
$129$	7.41641	−	22.8254i	0.652978	−	2.00966i
$130$	6.47214	+	4.70228i	0.567644	+	0.412417i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	−6.47214	−	4.70228i	−0.559107	−	0.406215i
$135$	2.47214	−	7.60845i	0.212768	−	0.654831i
$136$	−3.70820	−	11.4127i	−0.317976	−	0.978629i
$137$	8.09017	−	5.87785i	0.691190	−	0.502179i	−0.185861	−	0.982576i	$-0.559507\pi$
$137$	8.09017	−	5.87785i	0.691190	−	0.502179i	0.877051	+	0.480397i	$0.159507\pi$
$138$	6.47214	−	4.70228i	0.550945	−	0.400285i
$139$	−2.47214	−	7.60845i	−0.209684	−	0.645340i	−0.999488	−	0.0319820i	$-0.989818\pi$
$139$	−2.47214	−	7.60845i	−0.209684	−	0.645340i	0.789805	−	0.613359i	$-0.210182\pi$
$140$	−0.618034	+	1.90211i	−0.0522334	+	0.160758i
$141$	16.1803	+	11.7557i	1.36263	+	0.990009i
$142$	−12.0000			−1.00702
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−9.70820	−	7.05342i	−0.806222	−	0.585755i
$146$	−2.47214	+	7.60845i	−0.204595	+	0.629680i
$147$	0.618034	+	1.90211i	0.0509746	+	0.156884i
$148$	−4.85410	+	3.52671i	−0.399005	+	0.289894i
$149$	8.09017	−	5.87785i	0.662773	−	0.481532i	−0.204826	−	0.978798i	$-0.565663\pi$
$149$	8.09017	−	5.87785i	0.662773	−	0.481532i	0.867598	+	0.497266i	$0.165663\pi$
$150$	−0.618034	−	1.90211i	−0.0504623	−	0.155307i
$151$	−4.94427	+	15.2169i	−0.402359	+	1.23833i	0.520721	+	0.853727i	$0.325663\pi$
$151$	−4.94427	+	15.2169i	−0.402359	+	1.23833i	−0.923080	+	0.384607i	$0.874337\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	−20.0000			−1.60644
$156$	6.47214	+	4.70228i	0.518186	+	0.376484i
$157$	4.32624	−	13.3148i	0.345271	−	1.06264i	−0.616167	−	0.787616i	$-0.711315\pi$
$157$	4.32624	−	13.3148i	0.345271	−	1.06264i	0.961438	−	0.275020i	$-0.0886846\pi$
$158$	2.47214	+	7.60845i	0.196673	+	0.605296i
$159$	9.70820	−	7.05342i	0.769911	−	0.559373i
$160$	8.09017	−	5.87785i	0.639584	−	0.464685i
$161$	1.23607	+	3.80423i	0.0974158	+	0.299815i
$162$	−3.39919	+	10.4616i	−0.267065	+	0.821943i
$163$	6.47214	+	4.70228i	0.506937	+	0.368311i	0.811660	−	0.584130i	$-0.198564\pi$
$163$	6.47214	+	4.70228i	0.506937	+	0.368311i	−0.304724	+	0.952441i	$0.598564\pi$
$164$	−4.00000			−0.312348
$165$		0			0
$166$		0			0
$167$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$167$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$168$	1.85410	−	5.70634i	0.143047	−	0.440254i
$169$	0.927051	+	2.85317i	0.0713116	+	0.219475i
$170$	6.47214	−	4.70228i	0.496390	−	0.360649i
$171$		0			0
$172$	−3.70820	−	11.4127i	−0.282748	−	0.870209i
$173$	3.70820	−	11.4127i	0.281930	−	0.867690i	−0.705373	−	0.708837i	$-0.749220\pi$
$173$	3.70820	−	11.4127i	0.281930	−	0.867690i	0.987302	−	0.158853i	$-0.0507797\pi$
$174$	9.70820	+	7.05342i	0.735977	+	0.534719i
$175$	1.00000			0.0755929
$176$		0			0
$177$	4.00000			0.300658
$178$	4.85410	+	3.52671i	0.363830	+	0.264338i
$179$	3.70820	−	11.4127i	0.277164	−	0.853024i	−0.711474	−	0.702712i	$-0.751972\pi$
$179$	3.70820	−	11.4127i	0.277164	−	0.853024i	0.988639	−	0.150312i	$-0.0480277\pi$
$180$	0.618034	+	1.90211i	0.0460655	+	0.141775i
$181$	−8.09017	+	5.87785i	−0.601338	+	0.436897i	−0.846353	−	0.532622i	$-0.821207\pi$
$181$	−8.09017	+	5.87785i	−0.601338	+	0.436897i	0.245016	+	0.969519i	$0.421207\pi$
$182$	3.23607	−	2.35114i	0.239873	−	0.174278i
$183$		0			0
$184$	3.70820	−	11.4127i	0.273372	−	0.841354i
$185$	−9.70820	−	7.05342i	−0.713761	−	0.518578i
$186$	20.0000			1.46647
$187$		0			0
$188$	10.0000			0.729325
$189$	−3.23607	−	2.35114i	−0.235389	−	0.171020i
$190$		0			0
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	0.999789	−	0.0205267i	$-0.00653431\pi$
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	−0.820912	+	0.571055i	$0.806534\pi$
$192$	−11.3262	+	8.22899i	−0.817401	+	0.593876i
$193$	11.3262	−	8.22899i	0.815280	−	0.592336i	−0.100076	−	0.994980i	$-0.531909\pi$
$193$	11.3262	−	8.22899i	0.815280	−	0.592336i	0.915357	+	0.402644i	$0.131909\pi$
$194$	−3.09017	−	9.51057i	−0.221861	−	0.682819i
$195$	−4.94427	+	15.2169i	−0.354067	+	1.08971i
$196$	0.809017	+	0.587785i	0.0577869	+	0.0419847i
$197$	22.0000			1.56744			0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000			1.56744			0.783718	+	0.621117i	$0.213321\pi$
$198$		0			0
$199$	−18.0000			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$200$	−2.42705	−	1.76336i	−0.171618	−	0.124688i
$201$	4.94427	−	15.2169i	0.348742	−	1.07332i
$202$	−1.23607	−	3.80423i	−0.0869694	−	0.267664i
$203$	−4.85410	+	3.52671i	−0.340691	+	0.247527i
$204$	6.47214	−	4.70228i	0.453140	−	0.329226i
$205$	−2.47214	−	7.60845i	−0.172661	−	0.531397i
$206$	4.32624	−	13.3148i	0.301423	−	0.927685i
$207$	3.23607	+	2.35114i	0.224922	+	0.163416i
$208$	−4.00000			−0.277350
$209$		0			0
$210$	4.00000			0.276026
$211$	9.70820	+	7.05342i	0.668340	+	0.485578i	0.869469	−	0.493987i	$-0.164461\pi$
$211$	9.70820	+	7.05342i	0.668340	+	0.485578i	−0.201129	+	0.979565i	$0.564461\pi$
$212$	1.85410	−	5.70634i	0.127340	−	0.391913i
$213$	−7.41641	−	22.8254i	−0.508164	−	1.56397i
$214$	−9.70820	+	7.05342i	−0.663639	+	0.482162i
$215$	19.4164	−	14.1068i	1.32419	−	0.962079i
$216$	3.70820	+	11.4127i	0.252311	+	0.776534i
$217$	−3.09017	+	9.51057i	−0.209774	+	0.645619i
$218$	11.3262	+	8.22899i	0.767110	+	0.557338i
$219$	−16.0000			−1.08118
$220$		0			0
$221$	16.0000			1.07628
$222$	9.70820	+	7.05342i	0.651572	+	0.473395i
$223$	6.79837	−	20.9232i	0.455253	−	1.40112i	−0.415585	−	0.909554i	$-0.636423\pi$
$223$	6.79837	−	20.9232i	0.455253	−	1.40112i	0.870838	−	0.491570i	$-0.163577\pi$
$224$	−1.54508	−	4.75528i	−0.103235	−	0.317726i
$225$	0.809017	−	0.587785i	0.0539345	−	0.0391857i
$226$	−14.5623	+	10.5801i	−0.968670	+	0.703780i
$227$	3.70820	+	11.4127i	0.246122	+	0.757486i	0.995450	+	0.0952867i	$0.0303768\pi$
$227$	3.70820	+	11.4127i	0.246122	+	0.757486i	−0.749328	+	0.662199i	$0.769623\pi$
$228$		0			0
$229$	−14.5623	−	10.5801i	−0.962304	−	0.699155i	−0.00861950	−	0.999963i	$-0.502744\pi$
$229$	−14.5623	−	10.5801i	−0.962304	−	0.699155i	−0.953685	+	0.300808i	$0.902744\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	18.0000			1.18176
$233$	14.5623	+	10.5801i	0.954008	+	0.693128i	0.951752	−	0.306870i	$-0.0992816\pi$
$233$	14.5623	+	10.5801i	0.954008	+	0.693128i	0.00225687	+	0.999997i	$0.499282\pi$
$234$	1.23607	−	3.80423i	0.0808043	−	0.248690i
$235$	6.18034	+	19.0211i	0.403161	+	1.24080i
$236$	1.61803	−	1.17557i	0.105325	−	0.0765231i
$237$	−12.9443	+	9.40456i	−0.840821	+	0.610892i
$238$	−1.23607	−	3.80423i	−0.0801224	−	0.246591i
$239$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$239$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$240$	−3.23607	−	2.35114i	−0.208887	−	0.151765i
$241$	−20.0000			−1.28831			−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000			−1.28831			−0.644157	+	0.764894i	$0.722792\pi$
$242$		0			0
$243$	−10.0000			−0.641500
$244$		0			0
$245$	−0.618034	+	1.90211i	−0.0394847	+	0.121522i
$246$	2.47214	+	7.60845i	0.157618	+	0.485097i
$247$		0			0
$248$	24.2705	−	17.6336i	1.54118	−	1.11973i
$249$		0			0
$250$	3.70820	−	11.4127i	0.234527	−	0.721801i
$251$	1.61803	+	1.17557i	0.102129	+	0.0742014i	0.637678	−	0.770303i	$-0.279895\pi$
$251$	1.61803	+	1.17557i	0.102129	+	0.0742014i	−0.535548	+	0.844504i	$0.679895\pi$
$252$	1.00000			0.0629941
$253$		0			0
$254$	8.00000			0.501965
$255$	12.9443	+	9.40456i	0.810602	+	0.588937i
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	−4.32624	−	13.3148i	−0.269863	−	0.830554i	−0.990533	−	0.137275i	$-0.956166\pi$
$257$	−4.32624	−	13.3148i	−0.269863	−	0.830554i	0.720670	−	0.693279i	$-0.243834\pi$
$258$	−19.4164	+	14.1068i	−1.20881	+	0.878254i
$259$	−4.85410	+	3.52671i	−0.301619	+	0.219139i
$260$	2.47214	+	7.60845i	0.153315	+	0.471856i
$261$	−1.85410	+	5.70634i	−0.114766	+	0.353214i
$262$	−9.70820	−	7.05342i	−0.599775	−	0.435762i
$263$	8.00000			0.493301			0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000			0.493301			0.246651	+	0.969104i	$0.420670\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	−3.70820	+	11.4127i	−0.226938	+	0.698445i
$268$	−2.47214	−	7.60845i	−0.151010	−	0.464760i
$269$	−8.09017	+	5.87785i	−0.493266	+	0.358379i	−0.806439	−	0.591317i	$-0.798608\pi$
$269$	−8.09017	+	5.87785i	−0.493266	+	0.358379i	0.313173	+	0.949696i	$0.398608\pi$
$270$	−6.47214	+	4.70228i	−0.393882	+	0.286172i
$271$	−1.23607	−	3.80423i	−0.0750858	−	0.231090i	0.906469	−	0.422273i	$-0.138768\pi$
$271$	−1.23607	−	3.80423i	−0.0750858	−	0.231090i	−0.981554	+	0.191183i	$0.938768\pi$
$272$	−1.23607	+	3.80423i	−0.0749476	+	0.230665i
$273$	6.47214	+	4.70228i	0.391711	+	0.284595i
$274$	−10.0000			−0.604122
$275$		0			0
$276$	8.00000			0.481543
$277$	−17.7984	−	12.9313i	−1.06940	−	0.776965i	−0.0935962	−	0.995610i	$-0.529836\pi$
$277$	−17.7984	−	12.9313i	−1.06940	−	0.776965i	−0.975804	+	0.218645i	$0.929836\pi$
$278$	−2.47214	+	7.60845i	−0.148269	+	0.456325i
$279$	3.09017	+	9.51057i	0.185004	+	0.569383i
$280$	4.85410	−	3.52671i	0.290088	−	0.210761i
$281$	−4.85410	+	3.52671i	−0.289571	+	0.210386i	−0.723081	−	0.690763i	$-0.757275\pi$
$281$	−4.85410	+	3.52671i	−0.289571	+	0.210386i	0.433510	+	0.901149i	$0.357275\pi$
$282$	−6.18034	−	19.0211i	−0.368034	−	1.13269i
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	−0.907573	−	0.419894i	$-0.862067\pi$
$283$	1.23607	−	3.80423i	0.0734766	−	0.226138i	0.981050	+	0.193756i	$0.0620672\pi$
$284$	−9.70820	−	7.05342i	−0.576076	−	0.418544i
$285$		0			0
$286$		0			0
$287$	−4.00000			−0.236113
$288$	−4.04508	−	2.93893i	−0.238359	−	0.173178i
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$	3.70820	+	11.4127i	0.217753	+	0.670176i
$291$	16.1803	−	11.7557i	0.948508	−	0.689132i
$292$	−6.47214	+	4.70228i	−0.378753	+	0.275180i
$293$	−7.41641	−	22.8254i	−0.433271	−	1.33347i	−0.894848	−	0.446371i	$-0.852716\pi$
$293$	−7.41641	−	22.8254i	−0.433271	−	1.33347i	0.461577	−	0.887100i	$-0.347284\pi$
$294$	0.618034	−	1.90211i	0.0360445	−	0.110933i
$295$	3.23607	+	2.35114i	0.188411	+	0.136889i
$296$	18.0000			1.04623
$297$		0			0
$298$	−10.0000			−0.579284
$299$	12.9443	+	9.40456i	0.748587	+	0.543880i
$300$	0.618034	−	1.90211i	0.0356822	−	0.109819i
$301$	−3.70820	−	11.4127i	−0.213737	−	0.657816i
$302$	12.9443	−	9.40456i	0.744859	−	0.541172i
$303$	6.47214	−	4.70228i	0.371814	−	0.270139i
$304$		0			0
$305$		0			0
$306$	−3.23607	−	2.35114i	−0.184994	−	0.134406i
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$	28.0000			1.59286
$310$	16.1803	+	11.7557i	0.918982	+	0.667679i
$311$	−5.56231	+	17.1190i	−0.315409	+	0.970730i	0.660176	+	0.751111i	$0.270482\pi$
$311$	−5.56231	+	17.1190i	−0.315409	+	0.970730i	−0.975586	+	0.219620i	$0.929518\pi$
$312$	−7.41641	−	22.8254i	−0.419871	−	1.29223i
$313$	−1.61803	+	1.17557i	−0.0914567	+	0.0664472i	−0.632574	−	0.774500i	$-0.718002\pi$
$313$	−1.61803	+	1.17557i	−0.0914567	+	0.0664472i	0.541117	+	0.840947i	$0.318002\pi$
$314$	−11.3262	+	8.22899i	−0.639177	+	0.464389i
$315$	0.618034	+	1.90211i	0.0348223	+	0.107172i
$316$	−2.47214	+	7.60845i	−0.139069	+	0.428009i
$317$	1.61803	+	1.17557i	0.0908778	+	0.0660266i	0.632296	−	0.774727i	$-0.282113\pi$
$317$	1.61803	+	1.17557i	0.0908778	+	0.0660266i	−0.541418	+	0.840753i	$0.682113\pi$
$318$	−12.0000			−0.672927
$319$		0			0
$320$	−14.0000			−0.782624
$321$	−19.4164	−	14.1068i	−1.08372	−	0.787367i
$322$	1.23607	−	3.80423i	0.0688834	−	0.212001i
$323$		0			0
$324$	−8.89919	+	6.46564i	−0.494399	+	0.359202i
$325$	3.23607	−	2.35114i	0.179505	−	0.130418i
$326$	−2.47214	−	7.60845i	−0.136919	−	0.421393i
$327$	−8.65248	+	26.6296i	−0.478483	+	1.47262i
$328$	9.70820	+	7.05342i	0.536046	+	0.389460i
$329$	10.0000			0.551318
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$		0			0
$333$	−1.85410	+	5.70634i	−0.101604	+	0.312705i
$334$		0			0
$335$	12.9443	−	9.40456i	0.707221	−	0.513826i
$336$	−1.61803	+	1.17557i	−0.0882710	+	0.0641326i
$337$	4.32624	+	13.3148i	0.235665	+	0.725303i	0.997032	+	0.0769821i	$0.0245284\pi$
$337$	4.32624	+	13.3148i	0.235665	+	0.725303i	−0.761367	+	0.648321i	$0.775472\pi$
$338$	0.927051	−	2.85317i	0.0504249	−	0.155192i
$339$	−29.1246	−	21.1603i	−1.58183	−	1.14927i
$340$	8.00000			0.433861
$341$		0			0
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−11.1246	+	34.2380i	−0.599799	+	1.84599i
$345$	4.94427	+	15.2169i	0.266191	+	0.819251i
$346$	−9.70820	+	7.05342i	−0.521916	+	0.379194i
$347$	−3.23607	+	2.35114i	−0.173721	+	0.126216i	−0.671248	−	0.741233i	$-0.734242\pi$
$347$	−3.23607	+	2.35114i	−0.173721	+	0.126216i	0.497527	+	0.867448i	$0.334242\pi$
$348$	3.70820	+	11.4127i	0.198781	+	0.611784i
$349$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$349$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$350$	−0.809017	−	0.587785i	−0.0432438	−	0.0314184i
$351$	−16.0000			−0.854017
$352$		0			0
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$	−3.23607	−	2.35114i	−0.171995	−	0.124962i
$355$	7.41641	−	22.8254i	0.393622	−	1.21144i
$356$	1.85410	+	5.70634i	0.0982672	+	0.302435i
$357$	6.47214	−	4.70228i	0.342542	−	0.248871i
$358$	−9.70820	+	7.05342i	−0.513095	+	0.372785i
$359$	4.94427	+	15.2169i	0.260949	+	0.803117i	0.992599	+	0.121437i	$0.0387504\pi$
$359$	4.94427	+	15.2169i	0.260949	+	0.803117i	−0.731650	+	0.681680i	$0.761250\pi$
$360$	1.85410	−	5.70634i	0.0977198	−	0.300750i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$	10.0000			0.525588
$363$		0			0
$364$	4.00000			0.209657
$365$	−12.9443	−	9.40456i	−0.677534	−	0.492257i
$366$		0			0
$367$	6.79837	+	20.9232i	0.354872	+	1.09218i	0.956084	+	0.293094i	$0.0946850\pi$
$367$	6.79837	+	20.9232i	0.354872	+	1.09218i	−0.601211	+	0.799090i	$0.705315\pi$
$368$	−3.23607	+	2.35114i	−0.168692	+	0.122562i
$369$	−3.23607	+	2.35114i	−0.168463	+	0.122396i
$370$	3.70820	+	11.4127i	0.192780	+	0.593317i
$371$	1.85410	−	5.70634i	0.0962602	−	0.296258i
$372$	16.1803	+	11.7557i	0.838912	+	0.609505i
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$		0			0
$375$	24.0000			1.23935
$376$	−24.2705	−	17.6336i	−1.25166	−	0.909381i
$377$	−7.41641	+	22.8254i	−0.381964	+	1.17557i
$378$	1.23607	+	3.80423i	0.0635765	+	0.195668i
$379$	6.47214	−	4.70228i	0.332451	−	0.241540i	−0.409019	−	0.912526i	$-0.634129\pi$
$379$	6.47214	−	4.70228i	0.332451	−	0.241540i	0.741470	+	0.670986i	$0.234129\pi$
$380$		0			0
$381$	4.94427	+	15.2169i	0.253303	+	0.779586i
$382$	2.47214	−	7.60845i	0.126485	−	0.389282i
$383$	−1.61803	−	1.17557i	−0.0826777	−	0.0600688i	0.545679	−	0.837995i	$-0.316272\pi$
$383$	−1.61803	−	1.17557i	−0.0826777	−	0.0600688i	−0.628356	+	0.777926i	$0.716272\pi$
$384$	−6.00000			−0.306186
$385$		0			0
$386$	−14.0000			−0.712581
$387$	−9.70820	−	7.05342i	−0.493496	−	0.358546i
$388$	3.09017	−	9.51057i	0.156880	−	0.482826i
$389$	1.85410	+	5.70634i	0.0940067	+	0.289323i	0.986994	−	0.160760i	$-0.0513945\pi$
$389$	1.85410	+	5.70634i	0.0940067	+	0.289323i	−0.892987	+	0.450083i	$0.851394\pi$
$390$	12.9443	−	9.40456i	0.655459	−	0.476219i
$391$	12.9443	−	9.40456i	0.654620	−	0.475609i
$392$	−0.927051	−	2.85317i	−0.0468231	−	0.144107i
$393$	7.41641	−	22.8254i	0.374108	−	1.15139i
$394$	−17.7984	−	12.9313i	−0.896669	−	0.651468i
$395$	−16.0000			−0.805047
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$	14.5623	+	10.5801i	0.729942	+	0.530334i
$399$		0			0
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	17.7984	−	12.9313i	0.888808	−	0.645757i	−0.0467587	−	0.998906i	$-0.514889\pi$
$401$	17.7984	−	12.9313i	0.888808	−	0.645757i	0.935567	+	0.353149i	$0.114889\pi$
$402$	−12.9443	+	9.40456i	−0.645602	+	0.469057i
$403$	12.3607	+	38.0423i	0.615729	+	1.89502i
$404$	1.23607	−	3.80423i	0.0614967	−	0.189267i
$405$	−17.7984	−	12.9313i	−0.884408	−	0.642560i
$406$	6.00000			0.297775
$407$		0			0
$408$	−24.0000			−1.18818
$409$	−19.4164	−	14.1068i	−0.960080	−	0.697539i	−0.00691035	−	0.999976i	$-0.502200\pi$
$409$	−19.4164	−	14.1068i	−0.960080	−	0.697539i	−0.953169	+	0.302437i	$0.902200\pi$
$410$	−2.47214	+	7.60845i	−0.122090	+	0.375755i
$411$	−6.18034	−	19.0211i	−0.304854	−	0.938243i
$412$	11.3262	−	8.22899i	0.558004	−	0.405413i
$413$	1.61803	−	1.17557i	0.0796182	−	0.0578460i
$414$	−1.23607	−	3.80423i	−0.0607494	−	0.186968i
$415$		0			0
$416$	−16.1803	−	11.7557i	−0.793306	−	0.576371i
$417$	−16.0000			−0.783523
$418$		0			0
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$	3.23607	+	2.35114i	0.157904	+	0.114724i
$421$	−4.32624	+	13.3148i	−0.210848	+	0.648923i	0.788574	+	0.614939i	$0.210819\pi$
$421$	−4.32624	+	13.3148i	−0.210848	+	0.648923i	−0.999422	+	0.0339839i	$0.989181\pi$
$422$	−3.70820	−	11.4127i	−0.180513	−	0.555560i
$423$	8.09017	−	5.87785i	0.393358	−	0.285791i
$424$	−14.5623	+	10.5801i	−0.707208	+	0.513817i
$425$	−1.23607	−	3.80423i	−0.0599581	−	0.184532i
$426$	−7.41641	+	22.8254i	−0.359326	+	1.10589i
$427$		0			0
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−24.0000			−1.15738
$431$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$431$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$432$	1.23607	−	3.80423i	0.0594703	−	0.183031i
$433$	−8.03444	−	24.7275i	−0.386111	−	1.18833i	−0.935671	−	0.352873i	$-0.885205\pi$
$433$	−8.03444	−	24.7275i	−0.386111	−	1.18833i	0.549561	−	0.835454i	$-0.314795\pi$
$434$	8.09017	−	5.87785i	0.388341	−	0.282146i
$435$	−19.4164	+	14.1068i	−0.930946	+	0.676371i
$436$	4.32624	+	13.3148i	0.207189	+	0.637663i
$437$		0			0
$438$	12.9443	+	9.40456i	0.618501	+	0.449367i
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$	−12.9443	−	9.40456i	−0.615696	−	0.447329i
$443$	1.23607	−	3.80423i	0.0587274	−	0.180744i	−0.917389	−	0.397991i	$-0.869708\pi$
$443$	1.23607	−	3.80423i	0.0587274	−	0.180744i	0.976117	+	0.217247i	$0.0697076\pi$
$444$	3.70820	+	11.4127i	0.175984	+	0.541622i
$445$	−9.70820	+	7.05342i	−0.460213	+	0.334364i
$446$	−17.7984	+	12.9313i	−0.842777	+	0.612314i
$447$	−6.18034	−	19.0211i	−0.292320	−	0.899669i
$448$	−2.16312	+	6.65740i	−0.102198	+	0.314532i
$449$	8.09017	+	5.87785i	0.381799	+	0.277393i	0.762087	−	0.647475i	$-0.224175\pi$
$449$	8.09017	+	5.87785i	0.381799	+	0.277393i	−0.380288	+	0.924868i	$0.624175\pi$
$450$	−1.00000			−0.0471405
$451$		0			0
$452$	−18.0000			−0.846649
$453$	25.8885	+	18.8091i	1.21635	+	0.883730i
$454$	3.70820	−	11.4127i	0.174035	−	0.535624i
$455$	2.47214	+	7.60845i	0.115896	+	0.356690i
$456$		0			0
$457$	−14.5623	+	10.5801i	−0.681196	+	0.494918i	−0.873754	−	0.486368i	$-0.838322\pi$
$457$	−14.5623	+	10.5801i	−0.681196	+	0.494918i	0.192558	+	0.981286i	$0.438322\pi$
$458$	5.56231	+	17.1190i	0.259909	+	0.799919i
$459$	−4.94427	+	15.2169i	−0.230779	+	0.710264i
$460$	6.47214	+	4.70228i	0.301765	+	0.219245i
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−4.85410	−	3.52671i	−0.225346	−	0.163723i
$465$	−12.3607	+	38.0423i	−0.573213	+	1.76417i
$466$	−5.56231	−	17.1190i	−0.257669	−	0.793023i
$467$	−24.2705	+	17.6336i	−1.12311	+	0.815984i	−0.984677	−	0.174389i	$-0.944205\pi$
$467$	−24.2705	+	17.6336i	−1.12311	+	0.815984i	−0.138428	+	0.990372i	$0.544205\pi$
$468$	3.23607	−	2.35114i	0.149587	−	0.108682i
$469$	−2.47214	−	7.60845i	−0.114153	−	0.351326i
$470$	6.18034	−	19.0211i	0.285078	−	0.877379i
$471$	−22.6525	−	16.4580i	−1.04377	−	0.758344i
$472$	−6.00000			−0.276172
$473$		0			0
$474$	16.0000			0.734904
$475$		0			0
$476$	1.23607	−	3.80423i	0.0566551	−	0.174366i
$477$	−1.85410	−	5.70634i	−0.0848935	−	0.261275i
$478$		0			0
$479$	3.23607	−	2.35114i	0.147860	−	0.107426i	−0.511396	−	0.859345i	$-0.670871\pi$
$479$	3.23607	−	2.35114i	0.147860	−	0.107426i	0.659256	+	0.751919i	$0.270871\pi$
$480$	−6.18034	−	19.0211i	−0.282093	−	0.868192i
$481$	−7.41641	+	22.8254i	−0.338159	+	1.04075i
$482$	16.1803	+	11.7557i	0.736994	+	0.535458i
$483$	8.00000			0.364013
$484$		0			0
$485$	20.0000			0.908153
$486$	8.09017	+	5.87785i	0.366978	+	0.266625i
$487$	−8.65248	+	26.6296i	−0.392081	+	1.20670i	0.539130	+	0.842222i	$0.318753\pi$
$487$	−8.65248	+	26.6296i	−0.392081	+	1.20670i	−0.931212	+	0.364479i	$0.881247\pi$
$488$		0			0
$489$	12.9443	−	9.40456i	0.585360	−	0.425289i
$490$	1.61803	−	1.17557i	0.0730953	−	0.0531069i
$491$	8.65248	+	26.6296i	0.390481	+	1.20178i	0.932426	+	0.361362i	$0.117688\pi$
$491$	8.65248	+	26.6296i	0.390481	+	1.20178i	−0.541945	+	0.840414i	$0.682312\pi$
$492$	−2.47214	+	7.60845i	−0.111452	+	0.343016i
$493$	19.4164	+	14.1068i	0.874471	+	0.635340i
$494$		0			0
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−9.70820	−	7.05342i	−0.435472	−	0.316389i
$498$		0			0
$499$	−4.94427	−	15.2169i	−0.221336	−	0.681202i	−0.998643	−	0.0520806i	$-0.983415\pi$
$499$	−4.94427	−	15.2169i	−0.221336	−	0.681202i	0.777307	−	0.629122i	$-0.216585\pi$
$500$	9.70820	−	7.05342i	0.434164	−	0.315439i
$501$		0			0
$502$	−0.618034	−	1.90211i	−0.0275842	−	0.0848955i
$503$	1.23607	−	3.80423i	0.0551135	−	0.169622i	−0.919711	−	0.392597i	$-0.871577\pi$
$503$	1.23607	−	3.80423i	0.0551135	−	0.169622i	0.974824	+	0.222975i	$0.0715768\pi$
$504$	−2.42705	−	1.76336i	−0.108109	−	0.0785461i
$505$	8.00000			0.355995
$506$		0			0
$507$	6.00000			0.266469
$508$	6.47214	+	4.70228i	0.287155	+	0.208630i
$509$	5.56231	−	17.1190i	0.246545	−	0.758787i	−0.748834	−	0.662758i	$-0.769386\pi$
$509$	5.56231	−	17.1190i	0.246545	−	0.758787i	0.995379	−	0.0960291i	$-0.0306142\pi$
$510$	−4.94427	−	15.2169i	−0.218936	−	0.673816i
$511$	−6.47214	+	4.70228i	−0.286310	+	0.208017i
$512$	8.89919	−	6.46564i	0.393292	−	0.285744i
$513$		0			0
$514$	−4.32624	+	13.3148i	−0.190822	+	0.587290i
$515$	22.6525	+	16.4580i	0.998187	+	0.725226i
$516$	−24.0000			−1.05654
$517$		0			0
$518$	6.00000			0.263625
$519$	−19.4164	−	14.1068i	−0.852286	−	0.619222i
$520$	7.41641	−	22.8254i	0.325231	−	1.00096i
$521$	1.85410	+	5.70634i	0.0812297	+	0.249999i	0.983421	−	0.181337i	$-0.0580424\pi$
$521$	1.85410	+	5.70634i	0.0812297	+	0.249999i	−0.902191	+	0.431336i	$0.858042\pi$
$522$	4.85410	−	3.52671i	0.212458	−	0.154360i
$523$	−16.1803	+	11.7557i	−0.707517	+	0.514041i	−0.882372	−	0.470553i	$-0.844054\pi$
$523$	−16.1803	+	11.7557i	−0.707517	+	0.514041i	0.174855	+	0.984594i	$0.444054\pi$
$524$	−3.70820	−	11.4127i	−0.161994	−	0.498565i
$525$	0.618034	−	1.90211i	0.0269732	−	0.0830150i
$526$	−6.47214	−	4.70228i	−0.282199	−	0.205029i
$527$	40.0000			1.74243
$528$		0			0
$529$	−7.00000			−0.304348
$530$	−9.70820	−	7.05342i	−0.421697	−	0.306381i
$531$	0.618034	−	1.90211i	0.0268204	−	0.0825447i
$532$		0			0
$533$	−12.9443	+	9.40456i	−0.560679	+	0.407357i
$534$	9.70820	−	7.05342i	0.420115	−	0.305231i
$535$	−7.41641	−	22.8254i	−0.320639	−	0.986826i
$536$	−7.41641	+	22.8254i	−0.320340	+	0.985905i
$537$	−19.4164	−	14.1068i	−0.837880	−	0.608755i
$538$	10.0000			0.431131
$539$		0			0
$540$	−8.00000			−0.344265
$541$	21.0344	+	15.2824i	0.904341	+	0.657042i	0.939577	−	0.342337i	$-0.111218\pi$
$541$	21.0344	+	15.2824i	0.904341	+	0.657042i	−0.0352361	+	0.999379i	$0.511218\pi$
$542$	−1.23607	+	3.80423i	−0.0530937	+	0.163406i
$543$	6.18034	+	19.0211i	0.265224	+	0.816275i
$544$	−16.1803	+	11.7557i	−0.693726	+	0.504022i
$545$	−22.6525	+	16.4580i	−0.970325	+	0.704983i
$546$	−2.47214	−	7.60845i	−0.105798	−	0.325612i
$547$	−8.65248	+	26.6296i	−0.369953	+	1.13860i	0.576868	+	0.816838i	$0.304275\pi$
$547$	−8.65248	+	26.6296i	−0.369953	+	1.13860i	−0.946821	+	0.321761i	$0.895725\pi$
$548$	−8.09017	−	5.87785i	−0.345595	−	0.251089i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	−19.4164	−	14.1068i	−0.826417	−	0.600427i
$553$	−2.47214	+	7.60845i	−0.105126	+	0.323544i
$554$	6.79837	+	20.9232i	0.288835	+	0.888943i
$555$	−19.4164	+	14.1068i	−0.824181	+	0.598802i
$556$	−6.47214	+	4.70228i	−0.274480	+	0.199421i
$557$	6.79837	+	20.9232i	0.288056	+	0.886546i	0.985466	+	0.169873i	$0.0543359\pi$
$557$	6.79837	+	20.9232i	0.288056	+	0.886546i	−0.697410	+	0.716673i	$0.745664\pi$
$558$	3.09017	−	9.51057i	0.130817	−	0.402614i
$559$	−38.8328	−	28.2137i	−1.64245	−	1.19331i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	6.00000			0.253095
$563$	25.8885	+	18.8091i	1.09107	+	0.792710i	0.979580	−	0.201055i	$-0.0644370\pi$
$563$	25.8885	+	18.8091i	1.09107	+	0.792710i	0.111492	+	0.993765i	$0.464437\pi$
$564$	6.18034	−	19.0211i	0.260239	−	0.800934i
$565$	−11.1246	−	34.2380i	−0.468016	−	1.44040i
$566$	−3.23607	+	2.35114i	−0.136022	+	0.0988258i
$567$	−8.89919	+	6.46564i	−0.373731	+	0.271531i
$568$	11.1246	+	34.2380i	0.466778	+	1.43660i
$569$	9.27051	−	28.5317i	0.388640	−	1.19611i	−0.545165	−	0.838329i	$-0.683533\pi$
$569$	9.27051	−	28.5317i	0.388640	−	1.19611i	0.933805	−	0.357782i	$-0.116467\pi$
$570$		0			0
$571$	20.0000			0.836974			0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000			0.836974			0.418487	+	0.908223i	$0.362561\pi$
$572$		0			0
$573$	16.0000			0.668410
$574$	3.23607	+	2.35114i	0.135071	+	0.0981347i
$575$	1.23607	−	3.80423i	0.0515476	−	0.158647i
$576$	2.16312	+	6.65740i	0.0901300	+	0.277391i
$577$	14.5623	−	10.5801i	0.606237	−	0.440457i	−0.241850	−	0.970314i	$-0.577754\pi$
$577$	14.5623	−	10.5801i	0.606237	−	0.440457i	0.848087	+	0.529857i	$0.177754\pi$
$578$	0.809017	−	0.587785i	0.0336507	−	0.0244486i
$579$	−8.65248	−	26.6296i	−0.359585	−	1.10669i
$580$	−3.70820	+	11.4127i	−0.153975	+	0.473886i
$581$		0			0
$582$	−20.0000			−0.829027
$583$		0			0
$584$	24.0000			0.993127
$585$	6.47214	+	4.70228i	0.267590	+	0.194415i
$586$	−7.41641	+	22.8254i	−0.306369	+	0.942907i
$587$	−0.618034	−	1.90211i	−0.0255090	−	0.0785086i	0.937492	−	0.348008i	$-0.113142\pi$
$587$	−0.618034	−	1.90211i	−0.0255090	−	0.0785086i	−0.963001	+	0.269499i	$0.913142\pi$
$588$	1.61803	−	1.17557i	0.0667266	−	0.0484797i
$589$		0			0
$590$	−1.23607	−	3.80423i	−0.0508881	−	0.156618i
$591$	13.5967	−	41.8465i	0.559295	−	1.72133i
$592$	−4.85410	−	3.52671i	−0.199502	−	0.144947i
$593$	32.0000			1.31408			0.657041	−	0.753855i	$-0.271808\pi$
$593$	32.0000			1.31408			0.657041	+	0.753855i	$0.271808\pi$
$594$		0			0
$595$	8.00000			0.327968
$596$	−8.09017	−	5.87785i	−0.331386	−	0.240766i
$597$	−11.1246	+	34.2380i	−0.455300	+	1.40127i
$598$	−4.94427	−	15.2169i	−0.202186	−	0.622265i
$599$	16.1803	−	11.7557i	0.661111	−	0.480325i	−0.205927	−	0.978567i	$-0.566021\pi$
$599$	16.1803	−	11.7557i	0.661111	−	0.480325i	0.867038	+	0.498242i	$0.166021\pi$
$600$	−4.85410	+	3.52671i	−0.198168	+	0.143977i
$601$	−8.65248	−	26.6296i	−0.352942	−	1.08624i	−0.957193	−	0.289450i	$-0.906528\pi$
$601$	−8.65248	−	26.6296i	−0.352942	−	1.08624i	0.604251	−	0.796794i	$-0.293472\pi$
$602$	−3.70820	+	11.4127i	−0.151135	+	0.465146i
$603$	−6.47214	−	4.70228i	−0.263566	−	0.191492i
$604$	16.0000			0.651031
$605$		0			0
$606$	−8.00000			−0.324978
$607$	32.3607	+	23.5114i	1.31348	+	0.954299i	0.999989	+	0.00470738i	$0.00149841\pi$
$607$	32.3607	+	23.5114i	1.31348	+	0.954299i	0.313491	+	0.949591i	$0.398502\pi$
$608$		0			0
$609$	3.70820	+	11.4127i	0.150264	+	0.462465i
$610$		0			0
$611$	32.3607	−	23.5114i	1.30917	−	0.951170i
$612$	−1.23607	−	3.80423i	−0.0499651	−	0.153777i
$613$	8.03444	−	24.7275i	0.324508	−	0.998733i	−0.647154	−	0.762359i	$-0.724041\pi$
$613$	8.03444	−	24.7275i	0.324508	−	0.998733i	0.971662	−	0.236374i	$-0.0759590\pi$
$614$	−16.1803	−	11.7557i	−0.652985	−	0.474422i
$615$	−16.0000			−0.645182
$616$		0			0
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−22.6525	−	16.4580i	−0.911216	−	0.662037i
$619$	4.32624	−	13.3148i	0.173886	−	0.535167i	−0.825695	−	0.564117i	$-0.809217\pi$
$619$	4.32624	−	13.3148i	0.173886	−	0.535167i	0.999581	+	0.0289507i	$0.00921657\pi$
$620$	6.18034	+	19.0211i	0.248208	+	0.763907i
$621$	−12.9443	+	9.40456i	−0.519436	+	0.377392i
$622$	14.5623	−	10.5801i	0.583895	−	0.424225i
$623$	1.85410	+	5.70634i	0.0742830	+	0.228620i
$624$	−2.47214	+	7.60845i	−0.0989646	+	0.304582i
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$	2.00000			0.0799361
$627$		0			0
$628$	−14.0000			−0.558661
$629$	19.4164	+	14.1068i	0.774183	+	0.562477i
$630$	0.618034	−	1.90211i	0.0246231	−	0.0757820i
$631$	−2.47214	−	7.60845i	−0.0984142	−	0.302888i	0.889714	−	0.456518i	$-0.150904\pi$
$631$	−2.47214	−	7.60845i	−0.0984142	−	0.302888i	−0.988128	+	0.153630i	$0.950904\pi$
$632$	19.4164	−	14.1068i	0.772343	−	0.561140i
$633$	19.4164	−	14.1068i	0.771733	−	0.560697i
$634$	−0.618034	−	1.90211i	−0.0245453	−	0.0755426i
$635$	−4.94427	+	15.2169i	−0.196207	+	0.603864i
$636$	−9.70820	−	7.05342i	−0.384955	−	0.279686i
$637$	4.00000			0.158486
$638$		0			0
$639$	−12.0000			−0.474713
$640$	−4.85410	−	3.52671i	−0.191875	−	0.139406i
$641$	−5.56231	+	17.1190i	−0.219698	+	0.676161i	0.779089	+	0.626914i	$0.215682\pi$
$641$	−5.56231	+	17.1190i	−0.219698	+	0.676161i	−0.998787	+	0.0492469i	$0.984318\pi$
$642$	7.41641	+	22.8254i	0.292702	+	0.900845i
$643$	−11.3262	+	8.22899i	−0.446663	+	0.324520i	−0.788277	−	0.615321i	$-0.789027\pi$
$643$	−11.3262	+	8.22899i	−0.446663	+	0.324520i	0.341614	+	0.939840i	$0.389027\pi$
$644$	3.23607	−	2.35114i	0.127519	−	0.0926479i
$645$	−14.8328	−	45.6507i	−0.584042	−	1.79750i
$646$		0			0
$647$	17.7984	+	12.9313i	0.699726	+	0.508381i	0.879843	−	0.475264i	$-0.157648\pi$
$647$	17.7984	+	12.9313i	0.699726	+	0.508381i	−0.180117	+	0.983645i	$0.557648\pi$
$648$	33.0000			1.29636
$649$		0			0
$650$	−4.00000			−0.156893
$651$	16.1803	+	11.7557i	0.634158	+	0.460742i
$652$	2.47214	−	7.60845i	0.0968163	−	0.297970i
$653$	−8.03444	−	24.7275i	−0.314412	−	0.967661i	−0.975996	−	0.217789i	$-0.930115\pi$
$653$	−8.03444	−	24.7275i	−0.314412	−	0.967661i	0.661584	−	0.749871i	$-0.269885\pi$
$654$	22.6525	−	16.4580i	0.885782	−	0.643558i
$655$	19.4164	−	14.1068i	0.758662	−	0.551200i
$656$	−1.23607	−	3.80423i	−0.0482603	−	0.148530i
$657$	−2.47214	+	7.60845i	−0.0964472	+	0.296834i
$658$	−8.09017	−	5.87785i	−0.315388	−	0.229143i
$659$	4.00000			0.155818			0.0779089	−	0.996960i	$-0.475176\pi$
$659$	4.00000			0.155818			0.0779089	+	0.996960i	$0.475176\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$	16.1803	+	11.7557i	0.628867	+	0.456898i
$663$	9.88854	−	30.4338i	0.384039	−	1.18195i
$664$		0			0
$665$		0			0
$666$	4.85410	−	3.52671i	0.188093	−	0.136657i
$667$	7.41641	+	22.8254i	0.287164	+	0.883801i
$668$		0			0
$669$	−35.5967	−	25.8626i	−1.37625	−	0.999904i
$670$	−16.0000			−0.618134
$671$		0			0
$672$	−10.0000			−0.385758
$673$	27.5066	+	19.9847i	1.06030	+	0.770354i	0.974144	−	0.225928i	$-0.0725414\pi$
$673$	27.5066	+	19.9847i	1.06030	+	0.770354i	0.0861567	+	0.996282i	$0.472541\pi$
$674$	4.32624	−	13.3148i	0.166640	−	0.512867i
$675$	1.23607	+	3.80423i	0.0475763	+	0.146425i
$676$	2.42705	−	1.76336i	0.0933481	−	0.0678214i
$677$	9.70820	−	7.05342i	0.373117	−	0.271085i	−0.385386	−	0.922756i	$-0.625932\pi$
$677$	9.70820	−	7.05342i	0.373117	−	0.271085i	0.758502	+	0.651671i	$0.225932\pi$
$678$	11.1246	+	34.2380i	0.427238	+	1.31490i
$679$	3.09017	−	9.51057i	0.118590	−	0.364982i
$680$	−19.4164	−	14.1068i	−0.744585	−	0.540973i
$681$	24.0000			0.919682
$682$		0			0
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$		0			0
$685$	6.18034	−	19.0211i	0.236139	−	0.726760i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−29.1246	+	21.1603i	−1.11117	+	0.807315i
$688$	9.70820	−	7.05342i	0.370122	−	0.268909i
$689$	−7.41641	−	22.8254i	−0.282543	−	0.869577i
$690$	4.94427	−	15.2169i	0.188225	−	0.579298i
$691$	37.2148	+	27.0381i	1.41572	+	1.02858i	0.992460	+	0.122569i	$0.0391133\pi$
$691$	37.2148	+	27.0381i	1.41572	+	1.02858i	0.423257	+	0.906010i	$0.360887\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	4.00000			0.151838
$695$	−12.9443	−	9.40456i	−0.491004	−	0.356735i
$696$	11.1246	−	34.2380i	0.421677	−	1.29779i
$697$	4.94427	+	15.2169i	0.187278	+	0.576381i
$698$		0			0
$699$	29.1246	−	21.1603i	1.10159	−	0.800355i
$700$	−0.309017	−	0.951057i	−0.0116797	−	0.0359466i
$701$	−6.79837	+	20.9232i	−0.256771	+	0.790260i	0.736705	+	0.676215i	$0.236381\pi$
$701$	−6.79837	+	20.9232i	−0.256771	+	0.790260i	−0.993476	+	0.114045i	$0.963619\pi$
$702$	12.9443	+	9.40456i	0.488550	+	0.354952i
$703$		0			0
$704$		0			0
$705$	40.0000			1.50649
$706$	24.2705	+	17.6336i	0.913433	+	0.663648i
$707$	1.23607	−	3.80423i	0.0464871	−	0.143073i
$708$	−1.23607	−	3.80423i	−0.0464543	−	0.142972i
$709$	27.5066	−	19.9847i	1.03303	−	0.750541i	0.0641181	−	0.997942i	$-0.479577\pi$
$709$	27.5066	−	19.9847i	1.03303	−	0.750541i	0.968913	+	0.247401i	$0.0795766\pi$
$710$	−19.4164	+	14.1068i	−0.728685	+	0.529420i
$711$	2.47214	+	7.60845i	0.0927123	+	0.285339i
$712$	5.56231	−	17.1190i	0.208456	−	0.641562i
$713$	32.3607	+	23.5114i	1.21192	+	0.880509i
$714$	−8.00000			−0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$		0			0
$718$	4.94427	−	15.2169i	0.184519	−	0.567890i
$719$	−1.85410	−	5.70634i	−0.0691463	−	0.212811i	0.910512	−	0.413482i	$-0.135688\pi$
$719$	−1.85410	−	5.70634i	−0.0691463	−	0.212811i	−0.979659	+	0.200672i	$0.935688\pi$
$720$	−1.61803	+	1.17557i	−0.0603006	+	0.0438109i
$721$	11.3262	−	8.22899i	0.421811	−	0.306464i
$722$	−5.87132	−	18.0701i	−0.218508	−	0.672499i
$723$	−12.3607	+	38.0423i	−0.459699	+	1.41481i
$724$	8.09017	+	5.87785i	0.300669	+	0.218449i
$725$	6.00000			0.222834
$726$		0			0
$727$	18.0000			0.667583			0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000			0.667583			0.333792	+	0.942647i	$0.391672\pi$
$728$	−9.70820	−	7.05342i	−0.359810	−	0.261417i
$729$	4.01722	−	12.3637i	0.148786	−	0.457916i
$730$	4.94427	+	15.2169i	0.182996	+	0.563203i
$731$	−38.8328	+	28.2137i	−1.43628	+	1.04352i
$732$		0			0
$733$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$733$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$734$	6.79837	−	20.9232i	0.250933	−	0.772291i
$735$	3.23607	+	2.35114i	0.119364	+	0.0867231i
$736$	−20.0000			−0.737210
$737$		0			0
$738$	4.00000			0.147242
$739$	3.23607	+	2.35114i	0.119041	+	0.0864881i	0.645713	−	0.763580i	$-0.276560\pi$
$739$	3.23607	+	2.35114i	0.119041	+	0.0864881i	−0.526672	+	0.850069i	$0.676560\pi$
$740$	−3.70820	+	11.4127i	−0.136316	+	0.419538i
$741$		0			0
$742$	−4.85410	+	3.52671i	−0.178200	+	0.129470i
$743$	6.47214	−	4.70228i	0.237440	−	0.172510i	−0.462702	−	0.886514i	$-0.653120\pi$
$743$	6.47214	−	4.70228i	0.237440	−	0.172510i	0.700142	+	0.714004i	$0.253120\pi$
$744$	−18.5410	−	57.0634i	−0.679747	−	2.09205i
$745$	6.18034	−	19.0211i	0.226430	−	0.696880i
$746$	21.0344	+	15.2824i	0.770126	+	0.559529i
$747$		0			0
$748$		0			0
$749$	−12.0000			−0.438470
$750$	−19.4164	−	14.1068i	−0.708987	−	0.515109i
$751$	−6.18034	+	19.0211i	−0.225524	+	0.694091i	0.772714	+	0.634754i	$0.218899\pi$
$751$	−6.18034	+	19.0211i	−0.225524	+	0.694091i	−0.998238	+	0.0593368i	$0.981101\pi$
$752$	3.09017	+	9.51057i	0.112687	+	0.346815i
$753$	3.23607	−	2.35114i	0.117929	−	0.0856803i
$754$	19.4164	−	14.1068i	0.707104	−	0.513741i
$755$	9.88854	+	30.4338i	0.359881	+	1.10760i
$756$	−1.23607	+	3.80423i	−0.0449554	+	0.138358i
$757$	8.09017	+	5.87785i	0.294042	+	0.213634i	0.725019	−	0.688729i	$-0.241831\pi$
$757$	8.09017	+	5.87785i	0.294042	+	0.213634i	−0.430977	+	0.902363i	$0.641831\pi$
$758$	−8.00000			−0.290573
$759$		0			0
$760$		0			0
$761$	−38.8328	−	28.2137i	−1.40769	−	1.02275i	−0.993653	−	0.112485i	$-0.964119\pi$
$761$	−38.8328	−	28.2137i	−1.40769	−	1.02275i	−0.414035	−	0.910261i	$-0.635881\pi$
$762$	4.94427	−	15.2169i	0.179112	−	0.551250i
$763$	4.32624	+	13.3148i	0.156620	+	0.482028i
$764$	6.47214	−	4.70228i	0.234154	−	0.170123i
$765$	6.47214	−	4.70228i	0.234001	−	0.170011i
$766$	0.618034	+	1.90211i	0.0223305	+	0.0687261i
$767$	2.47214	−	7.60845i	0.0892637	−	0.274725i
$768$	27.5066	+	19.9847i	0.992558	+	0.721136i
$769$	32.0000			1.15395			0.576975	−	0.816762i	$-0.304233\pi$
$769$	32.0000			1.15395			0.576975	+	0.816762i	$0.304233\pi$
$770$		0			0
$771$	−28.0000			−1.00840
$772$	−11.3262	−	8.22899i	−0.407640	−	0.296168i
$773$	−9.27051	+	28.5317i	−0.333437	+	1.02621i	0.634050	+	0.773292i	$0.281391\pi$
$773$	−9.27051	+	28.5317i	−0.333437	+	1.02621i	−0.967487	+	0.252921i	$0.918609\pi$
$774$	3.70820	+	11.4127i	0.133289	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.618034 - 1.90211i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.618034 - 1.90211i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-1.61803 + 1.17557i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-0.927051 + 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} -2.00000 q^{10} -2.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(-1.23607 - 3.80423i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-3.23607 + 2.35114i) q^{17} +(0.309017 + 0.951057i) q^{18} +(-1.61803 - 1.17557i) q^{20} -2.00000 q^{21} -4.00000 q^{23} +(4.85410 + 3.52671i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(1.23607 + 3.80423i) q^{26} +(3.23607 - 2.35114i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-1.23607 + 3.80423i) q^{30} +(-8.09017 - 5.87785i) q^{31} +5.00000 q^{32} +4.00000 q^{34} +(-1.61803 - 1.17557i) q^{35} +(-0.309017 + 0.951057i) q^{36} +(-1.85410 - 5.70634i) q^{37} +(-6.47214 + 4.70228i) q^{39} +(1.85410 + 5.70634i) q^{40} +(1.23607 - 3.80423i) q^{41} +(1.61803 + 1.17557i) q^{42} +12.0000 q^{43} -2.00000 q^{45} +(3.23607 + 2.35114i) q^{46} +(-3.09017 + 9.51057i) q^{47} +(-0.618034 - 1.90211i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(0.809017 - 0.587785i) q^{50} +(2.47214 + 7.60845i) q^{51} +(-1.23607 + 3.80423i) q^{52} +(4.85410 + 3.52671i) q^{53} -4.00000 q^{54} +3.00000 q^{56} +(-1.85410 + 5.70634i) q^{58} +(0.618034 + 1.90211i) q^{59} +(-3.23607 + 2.35114i) q^{60} +(3.09017 + 9.51057i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-5.66312 - 4.11450i) q^{64} -8.00000 q^{65} +8.00000 q^{67} +(3.23607 + 2.35114i) q^{68} +(-2.47214 + 7.60845i) q^{69} +(0.618034 + 1.90211i) q^{70} +(9.70820 - 7.05342i) q^{71} +(2.42705 - 1.76336i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(1.61803 + 1.17557i) q^{75} +8.00000 q^{78} +(-6.47214 - 4.70228i) q^{79} +(0.618034 - 1.90211i) q^{80} +(-3.39919 - 10.4616i) q^{81} +(-3.23607 + 2.35114i) q^{82} +(0.618034 + 1.90211i) q^{84} +(-2.47214 + 7.60845i) q^{85} +(-9.70820 - 7.05342i) q^{86} -12.0000 q^{87} -6.00000 q^{89} +(1.61803 + 1.17557i) q^{90} +(-1.23607 + 3.80423i) q^{91} +(1.23607 + 3.80423i) q^{92} +(-16.1803 + 11.7557i) q^{93} +(8.09017 - 5.87785i) q^{94} +(3.09017 - 9.51057i) q^{96} +(8.09017 + 5.87785i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + 3 q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 - 2 * q^6 + q^7 + 3 * q^8 - q^9	\( 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} - 2 q^{6} + q^{7} + 3 q^{8} - q^{9} - 8 q^{10} - 8 q^{12} - 4 q^{13} + q^{14} + 4 q^{15} + q^{16} - 4 q^{17} - q^{18} - 2 q^{20} - 8 q^{21} - 16 q^{23} + 6 q^{24} + q^{25} - 4 q^{26} + 4 q^{27} - q^{28} + 6 q^{29} + 4 q^{30} - 10 q^{31} + 20 q^{32} + 16 q^{34} - 2 q^{35} + q^{36} + 6 q^{37} - 8 q^{39} - 6 q^{40} - 4 q^{41} + 2 q^{42} + 48 q^{43} - 8 q^{45} + 4 q^{46} + 10 q^{47} + 2 q^{48} - q^{49} + q^{50} - 8 q^{51} + 4 q^{52} + 6 q^{53} - 16 q^{54} + 12 q^{56} + 6 q^{58} - 2 q^{59} - 4 q^{60} - 10 q^{62} + q^{63} - 7 q^{64} - 32 q^{65} + 32 q^{67} + 4 q^{68} + 8 q^{69} - 2 q^{70} + 12 q^{71} + 3 q^{72} + 8 q^{73} + 6 q^{74} + 2 q^{75} + 32 q^{78} - 8 q^{79} - 2 q^{80} + 11 q^{81} - 4 q^{82} - 2 q^{84} + 8 q^{85} - 12 q^{86} - 48 q^{87} - 24 q^{89} + 2 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} + 10 q^{94} - 10 q^{96} + 10 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 - 2 * q^6 + q^7 + 3 * q^8 - q^9 - 8 * q^10 - 8 * q^12 - 4 * q^13 + q^14 + 4 * q^15 + q^16 - 4 * q^17 - q^18 - 2 * q^20 - 8 * q^21 - 16 * q^23 + 6 * q^24 + q^25 - 4 * q^26 + 4 * q^27 - q^28 + 6 * q^29 + 4 * q^30 - 10 * q^31 + 20 * q^32 + 16 * q^34 - 2 * q^35 + q^36 + 6 * q^37 - 8 * q^39 - 6 * q^40 - 4 * q^41 + 2 * q^42 + 48 * q^43 - 8 * q^45 + 4 * q^46 + 10 * q^47 + 2 * q^48 - q^49 + q^50 - 8 * q^51 + 4 * q^52 + 6 * q^53 - 16 * q^54 + 12 * q^56 + 6 * q^58 - 2 * q^59 - 4 * q^60 - 10 * q^62 + q^63 - 7 * q^64 - 32 * q^65 + 32 * q^67 + 4 * q^68 + 8 * q^69 - 2 * q^70 + 12 * q^71 + 3 * q^72 + 8 * q^73 + 6 * q^74 + 2 * q^75 + 32 * q^78 - 8 * q^79 - 2 * q^80 + 11 * q^81 - 4 * q^82 - 2 * q^84 + 8 * q^85 - 12 * q^86 - 48 * q^87 - 24 * q^89 + 2 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 + 10 * q^94 - 10 * q^96 + 10 * q^97 + 4 * q^98

Introduction

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